From 1798 to 1800, the United States and France engaged in an undeclared naval war, often called the Quasi-War. This map represents just a fraction of the encounters between American and French vessels (I would estimate less than one of four). Most of the actions between American merchants and French armed vessels (both privateers and naval vessels) were not recorded with enough spatial detail to make a guess about where they happened.
This map plots encounters between French and American vessels from 1796 to 1800. Though the undeclared war did not start until 1798, the French were capturing American ships long before that time. The only thing that changed in 1798 was that American vessels could legally capture French vessels, and the American navy began cruising on the high seas.
For more about how I created this map, click here.
Carleton, Osgood, and William Norman. A new general chart of the West Indies. 1789. David Rumsey Historical Map Collection.